A Refreshingly Different Introduction to Calculus

The author of this book, Kalid Azad, is a math education blogger and a Princeton computer science graduate. He believes that starting calculus by immediately learning limits—which were only introduced 150 years after the initial development of calculus—is like asking a beginner to drive a Formula 1 race car without practice. In this book, Kalid Azad begins with the origins of calculus (Archimedes) and explains core concepts such as derivatives and integrals in the historical order of their development. The book utilizes numerous visual illustrations to clarify calculus-related ideas.

The difficulty of calculus courses has historical roots. Legend has it that Cambridge University once faced financial difficulties, during which many faculty members, including Isaac Newton, were months behind on their salaries. To address this, Newton separated calculus into a distinct subject and made it a mandatory course for the entire university, with a policy requiring students who failed to retake it the following year at their own expense until they passed. Soon after, the faculty salaries were paid.

Of course, this is just anecdotal hearsay, but the fact remains: calculus is notoriously difficult to learn and pass. The high difficulty level, coupled with outdated teaching methods (unchanged for many years), has been a persistent problem in calculus education.

This book is completely different from traditional calculus textbooks. It is based on the author’s more than a decade of reflections on calculus and his deep understanding of the subject. Kalid Azad aims to help readers grasp calculus in just a few hours, without mechanically memorizing formulas or doing excessive drills.

The book has received outstanding reviews, especially from students who struggle with traditional teaching methods. It helps readers understand the core concepts of calculus by first building intuition (through real-life calculus examples) and then systematically mastering rigorous theory, thus restoring confidence in learning calculus.

An online version of the book is available for direct preview: betterexplained.com/calculus/lesson-1